Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
304 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×Dic20 | C2 | semidirect |
| 3. C2×C5×#677 | C2 | semidirect |
| 4. C5×#4021 | C2 | semidirect |
| 5. C4×C52×C8 | C2 | semidirect |
| 16. #64985 | C5 | direct (N × H) |
| 31. C2×Dic20 | C2×C5 | semidirect |
| 33. C2×#677 | C2×C5 | semidirect |
| 34. #4021 | C2×C5 | semidirect |
| 36. C4×C5×C8 | D5 | semidirect |
| 37. C4×C5×C8 | C2×C5 | semidirect |
| 98. C4×C8 | C5×D5 | semidirect |
| 99. C52 | #495 | semidirect |
| 146. C5 | #64985 | direct (N × H) |
| 147. C5 | C5×#495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Dic20 | 2 |
| C2×C5×D40 | 2 |
| C2×C5×#677 | 2 |
| C5×#4021 | 2 |
| C4×C52×C8 | 2 |
| C5×#495 | 5 |
| #64985 | 5 |